I manage a small dairy farm and pretty much always have a folding box cutter on me, it cuts anything and the blades are about $0.04 a piece, for killing chickens my favorite tool is a small spined paring knife, victorinox does make a high quality very usable knife. If you don't feel like shelling out the cash for a good knife a box cutter works almost as well, I've had to bleed a cow out using a box cutter as well and i actually worked surprisingly well.